Finite Group Databasebeta

← #29577756

Subgroups — #29577756

Order 15616.

610 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450290C211yesmaximal, characteristic
2#21448420C211yesmaximal, characteristic, complemented
3#21445897C211yesmaximal, characteristic, complemented
4#21444349C211yesmaximal, characteristic
5#21444347C211yesmaximal, characteristic
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1284C211yesmaximal, characteristic, complemented
8C2×#14519761—21no—
9C2×#14519761—21no—
10C2×#14519751C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12#16839726C2211yescharacteristic
13#16839699—22no—
14#16839664C412yescomplemented
15#16839647—22no—
16#16839645—22no—
17#16839632C412yescomplemented
18#16839625C2211yescharacteristic
19#16839620—21no—
20C22⋊C4×Dic61—21no—
21#16839530—22no—
22#16839497—22no—
23#16839495—22no—
24C61×#407C2211yescharacteristic
25C61×#381C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C2×#11758194—21no—
32#14519761—44no—
33#14519761—44no—
34#14519751—21no—
35#14519751—21no—
36#14519751—21no—
37#14519751—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61C2×C412yes—
46C2×C4⋊Dic61D412yes—
47C2×#11758196—22no—
48C2×C22⋊Dic61—21no—
49C2×#11758198—21no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×C4×Dic61—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55#14519684—22no—
56#14519684—22no—
57#14519684—21no—
58#14519684D412yes—
59C23×C4×C61C2311yescharacteristic
60C2×M16×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C42×C61C2×C412yes—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#95×C61—21no—
67#95×C61—21no—
68#95×C61D412yes—
69C24×C61C2×D411yescharacteristic
70C23×D61—21no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—42no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—22no—
90C22×Dic61—42no—
91C22×Dic61—42no—
92C22×Dic61C22⋊C412yes—
93C22×Dic61C22⋊C412yes—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—42no—
97M16×C61—42no—
98C2×C8×C61—41no—
99C22⋊C4×C61—24no—
100C22⋊C4×C61—42no—
101C42×C61—42no—
102C22⋊Dic61—42no—
103#11758198—44no—
104#11758198—44no—
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—22no—
108C4⋊Dic61—22no—
109C4⋊Dic61—22no—
110C4⋊Dic61—22no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—44no—
114C4⋊Dic61—44no—
115#11758196—82no—
116C4×Dic61—82no—
117#11758194—42no—
118C2×#92418—41no—
119C23×C61—22no—
120C23×C61—22no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61#12011yescharacteristic
124C23×C61#12311yescharacteristic
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—42no—
128C22×D61—41no—
129C22×D61—42no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—24no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C22⋊D61—82no—
147C22⋊D61—82no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—42no—
160C2×Dic61—81no—
161C2×Dic61—81no—
162D244—81no—
163D244—81no—
164C8×C61—81no—
165#92418—81no—
166#9464—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—44no—
175C22×C61#38611yescharacteristic
176C22×C61#41012yes—
177C22×C61#45312yes—
178C2×D61—82no—
179C2×D61—82no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—44no—
188C4×C61—82no—
189Dic61—42no—
190Dic61—42no—
191Dic61—82no—
192Dic61—81no—
193#2501—611no—
194#2313—611no—
195#1821—611no—
196#1510—611no—
197#1510—611no—
198#1284—611no—
199#1284D6111yescharacteristic, complemented
200C2×C61—22no—
201C2×C61—22no—
202C2×C61—41no—
203C2×C61#188711yescharacteristic
204C2×C61#189911yescharacteristic
205C2×C61#191211yescharacteristic
206D61—161no—
207C2×#123—1221no—
208C2×#123—1221no—
209C2×#121—611no—
210C22×C4⋊C4—611no—
211#407—611no—
212#407C2×D6111yescharacteristic
213#399—1222no—
214#390—612no—
215#387—1222no—
216#387—1222no—
217#384—612no—
218#381—611no—
219#381C2×D6111yescharacteristic
220#380—1221no—
221C4×C22⋊C4—1221no—
222C4×C22⋊C4C2×D6111yescharacteristic
223#343—1222no—
224#327—1222no—
225#327—1222no—
226C61#946411yescharacteristic, complemented, Sylow
227C22×D4—611no—
228C22×D4—1221no—
229C23×C4—611no—
230C23×C4—611no—
231C23×C4C22×D6111yescharacteristic
232C2×M16—21no—
233C2×M16—1221no—
234#123—2444no—
235#123—2444no—
236#121—1221no—
237#121—1221no—
238#121—1221no—
239#121—1221no—
240C2×C4⋊C4—612no—
241C2×C4⋊C4—612no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1222no—
248C2×C4⋊C4—1222no—
249C2×C4⋊C4—1222no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—1222no—
253C2×C22⋊C4—1222no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C42—1222no—
257C2×C42C4×D6112yes—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8—1221no—
261C22⋊C8—1221no—
262#95—21no—
263#95—21no—
264#95—612no—
265#95—1222no—
266#95—1222no—
267#95—1221no—
268#95D24412yes—
269C24—1221no—
270C24D4×D6111yescharacteristic
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2442no—
274C2×D4—2442no—
275C2×D4—2442no—
276C2×D4—2441no—
277C2×D4—2441no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—42no—
281C22×C4—612no—
282C22×C4—612no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1222no—
289C22×C4—2442no—
290C22×C4—2442no—
291C22×C4C2×C4×D6111yescharacteristic
292C22×C4C2×D24411yescharacteristic
293C22×C4#1175822211yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4#1175822611yescharacteristic
297M16—42no—
298M16—2442no—
299C2×C8—41no—
300C2×C8—2441no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—1222no—
304C4⋊C4—1222no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—4882no—
308C4⋊C4—2444no—
309C4⋊C4—2444no—
310C22⋊C4—24no—
311C22⋊C4—42no—
312C22⋊C4—2444no—
313C22⋊C4—2444no—
314C22⋊C4—2442no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42—42no—
318C42—4882no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23—2441no—
323C23—2441no—
324C23—2442no—
325C23—2442no—
326C23—2441no—
327C23C22⋊C4×D6111yescharacteristic
328C23#1451974711yescharacteristic
329C23#1451976211yescharacteristic
330D4—4881no—
331D4—4881no—
332D4—4882no—
333D4—4882no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—4881no—
349C2×C4—4881no—
350C2×C4—2442no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2442no—
354C2×C4—2441no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4#1451973911yescharacteristic
361C2×C4C4×D24411yescharacteristic
362C2×C4#1451975011yescharacteristic
363C2×C4#1451975211yescharacteristic
364C8—81no—
365C8—4881no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—44no—
374C22—4882no—
375C22—4882no—
376C22—4881no—
377C22—4881no—
378C22—4881no—
379C22#1683964011yescharacteristic
380C22#1683973412yes—
381C22#1683993112yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—44no—
387C4—82no—
388C4—4882no—
389C4—4881no—
390C4—2442no—
391C4—2442no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—9761no—
396C2#2144621611yescharacteristic
397C2#2144627611yescharacteristic
398C2#2144635511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1284C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1284D61
hypocenterC61#9464
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21448420C2semidirect
3. #21445897C2semidirect
6. #21443672C2semidirect
7. C61×#1284C2semidirect
14. #16839664C4semidirect
17. #16839632C4semidirect
199. #1284D61semidirect
226. C61#9464semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214502902
#214484202
#214458972
#214443492
#214443472
#214436722
C61×#12842
#946461